Non-volatile memory devices, such as a flash memory card, are typically made of multiple memory chips packaged together with a controller chip. The performance of such devices can be increased by operating greater numbers of these memory chips in parallel. Such parallelism is usually constrained by the ability of a hosting device, such as a laptop computer, to supply power, both in terms of average power consumption levels and in terms of peak current levels. For example, a memory device may have four or eight memory chips and, in terms of average power consumption, could operate most or all of these in parallel; however, to be able to cover spikes in peak current levels, the device will often itself to operations on no more than two devices at the same time in order to avoid concurrent peaks in current demands that could exceed the supply's capability and lead to errors in operation. Consequently, these and similar devices would benefit from techniques to allow concurrent operations on more chips in parallel while still not exceeding the supply's ability to meet the device's requirements.